Study On Quantized Feedback Variable Structure Control For Uncertain Systems

In the traditional control systems, the output signals of the plant usually are lossless delivered directly to the actuator. In this process, there are no data loss or approximation. With the rapid development of modern control technology, a number of digital processing facilities are widely utilized in the control systems. It needs to convert signals between analog ones with digital ones. In such case, it cannot make the conversion of the in-formation at any high accuracy. In addition, due to the limited transmission capacity of the channel, it requires to handle signals for reducing the size of the data packets before transmission. The signal quantization problem has become an important research topic in these areas. On the other hand, the system modeling often ignores the influence of model uncertainties and external disturbances, thus the problem of system robustness is neces-sary to be fully taken into account in the theoretical study, in which variable structure control is a well known robust technology to deal with model uncertainties and external disturbances.This dissertation presents the quantized feedback control design method via variable structure control technique. Combined with the static adjustment policy of the quan-tization parameter, a systematically new quantized feedback variable structure control schemes are presented. For a class of single input linear uncertain systems, a static ad-justment law of the parameter of the dynamic quantizer is provided and then the reaching law of quantized feedback variable structure is given. Compared with the existing result, the proposed method can obtain better convergence performance and be convenient to use in practical engineering; Based on sliding sector approach, with the designed static updating policy of the quantization parameter, the proposed quantized feedback variable structure control strategy can effectively avoid the occur of chattering phenomenon and obtain quadratic stability of the closed-loop system; By introducing the switching mech-anism, a quantized feedback variable structure control design method is presented for a class of linear uncertain planar systems. It can effectively overcome the effects of model uncertainties and satisfy the limitations of quantized measurement saturation; For a class of uncertain systems subject to input nonlinearity, combined with the adjustment of the quantization parameters, the proposed quantized output feedback variable controller can ensure that the system trajectories asymptotically converge to the specified sliding sur-face; Finally, based on the aforementioned work, the results further are extended to a class multi-input linear systems with matched/mismatched uncertainties. All the main results are verified by simulation and part of the developed theories is applied to the simulation studies of aircraft model. The main research contents are outlined as follows:Chapters1-2summarize and analyze the background and the development of quan-tized control and variable structure control. Preliminaries about the considered problem are also given.In Chapter3, based on sliding mode variable structure control strategy, the quantized feedback stabilization problem for a class of single input linear uncertain systems is inves-tigated. It is assumed that the system input signal and state signals are quantized before they are transmitted over the digital communications channel. For the dynamic quantizer, a static adjustment strategy of the adjustable quantization parameter is presented. With the quantization parameter adjustment, the designed sliding mode variable structure control scheme ensure that the system state to reach and maintain on the desired sliding surface, thus it improves the existing result that the controller proposed by using a complex time-varying sliding surface can merely guarantee that the state trajectories to some neighbor of the switching surface, and as a result, only practical stability is obtained. Finally, the effectiveness of the proposed method is validated by a numerical example.In Chapter4, based on the results in Chapter3, a chattering free quantized feedback variable structure controller design method is provided. First, based on sliding sector tech-nique, a quantization parameter adjustment scheme related to sliding sector is presented, then with the adjustment policy of the quantization parameter, the designed quantized feedback variable structure control law can guarantee the system trajectories enter the in-ner sector from the outside of the sliding sector, thus quadratic stability of the closed-loop system can be achieved without the occurrence of the chattering phenomenon. Finally, a numerical example shows the effectiveness of the proposed method.In Chapter5, the quantized feedback stabilization problem of planar systems in the presence of saturating quantized measurements is concerned. A novel switching-based sliding mode variable structure quantized feedback controller design method is presented. First, by introducing two switching lines, s1(x)=0and s2(x)=0, a partition of the state space, which is composed of several sector sets, is formed, and then the adjustment policy of the quantization parameter is developed in each sector set. With the designed adjust-ment policy of the quantization parameter, the proposed quantized feedback sliding mode control strategy can ensure the state trajectories to the desired switching line, and then global robust stabilization of the closed-loop system is guaranteed. The proposed method can not only make full use of the advantage of the variable structure control on effectively overcome the influence of the system model uncertainties and external disturbances, but also meet the quantized saturation requirement. Finally, a numerical example illustrates the effectiveness and superiority of the proposed method in this chapter.In Chapter6, based on sliding mode variable structure control technique, the quan-tized output feedback control scheme for a class of uncertain systems with non-smooth nonlinearities (dead zone and saturation) in the actuator device is presented. It is assumed that system signals, including the system input and output signals and the estimated state signals of the dynamic compensator, are quantized before being transmitted through com-munication channels. First, a dynamical compensator is developed to estimate unmeasur-able system state, then a sliding surface, in the augmented space using the system output and the estimated state, is proposed. Next, an adaptive sliding mode variable structure control scheme with a static adjustment law of the quantization parameter is established. It is proved that the designed method can tackle system model uncertainties and non-symmetric input nonlinearity simultaneously and ensures that the system trajectory to converge to the specified sliding surface asymptotically. Finally, the proposed method is applied to model aircraft simulation to verify the validity of the proposed method in this chapter.In Chapter7, for a class of multi-input linear uncertain systems, the quantized feed-back variable structure control design problem is investigated. Compared to Chapter3and Chapter4, the considered system is extended from the matched uncertainty of single-input linear systems to include matched/mismatched uncertainty in multi-input linear sys-tems, and consider quantized saturating requirements. In addition, compared to Chapter5, the system is extended from2dimensional single-input linear systems to n dimensional multi-input linear systems. Finally, a numerical example illustrates the effectiveness of the proposed method in this chapter.Finally, the results of the dissertation are summarized and further research topics are pointed out.